57 research outputs found
A theorem on fractional ID -- factor-critical graphs
Let , and be three nonnegative integers with , let be a graph of order satisfying the inequality , and let and be two integer-valued functions defined on satisfying for every . A graph is said to be fractional ID--factor-critical if contains a fractional -factor for every independent set of . In this paper, we prove that is fractional ID--factor-critical if \operatorname{bind}(G)((a+r)p - (a+b-2)) > (2a+b+r-1)(p-1), which is a generalization of a previous result of Zhou
Spectral radius and k-factor-critical graphs
For a nonnegative integer , a graph is said to be -factor-critical
if admits a perfect matching for any with . In
this article, we prove spectral radius conditions for the existence of
-factor-critical graphs. Our result generalises one previous result on
perfect matchings of graphs. Furthermore, we claim that the bounds on spectral
radius in Theorem 3.1 are sharp.Comment: 12 page
Network-Structured BST/MBO Composites Made from Core-Shell-Structured Granulates
A finite element method (FEM)-based simulation approach to predict the tunability in composite materials was developed and tested with analytical data. These tests showed good prediction capabilities of the simulation for the test data. The simulation model was then used to predict the tunability of a network-structured composite, where the dielectric phase formed clusters in a paraelectric network. This was achieved by simulating a reciprocal core-shell unit cell of said network. The simulation showed a high tunability for this network model, exceeding the tunability of the analytically evaluated layered, columnar, and particulate model. The simulation results were experimentally verified with a Ba0.6Sr0.4TiO3/Mg3B2O6 (BST/MBO) composite, where core-shell granulates were made with a two-step granulation process. These structured samples showed higher tunability and dielectric loss than the unstructured samples made for comparison. Overall, the structured samples showed higher tunability to loss ratios, indicating their potential for use in tunable radio frequency applications, since they may combine high performance with little energy loss
Network-Structured BST/MBO Composites Made from Core-Shell-Structured Granulates
A finite element method (FEM)-based simulation approach to predict the tunability in composite materials was developed and tested with analytical data. These tests showed good prediction capabilities of the simulation for the test data. The simulation model was then used to predict the tunability of a network-structured composite, where the dielectric phase formed clusters in a paraelectric network. This was achieved by simulating a reciprocal core-shell unit cell of said network. The simulation showed a high tunability for this network model, exceeding the tunability of the analytically evaluated layered, columnar, and particulate model. The simulation results were experimentally verified with a Ba₀.₆Sr₀.₄TiO₃/Mg₃B₂O₆ (BST/MBO) composite, where core-shell granulates were made with a two-step granulation process. These structured samples showed higher tunability and dielectric loss than the unstructured samples made for comparison. Overall, the structured samples showed higher tunability to loss ratios, indicating their potential for use in tunable radio frequency applications, since they may combine high performance with little energy loss
A neighborhood condition for graphs to have restricted fractional (g,f)-factors
Let be a function defined on with for any . Set . If for every , then we call the graph with vertex set and edge set a fractional -factor of with indicator function , where E_h=\{e:e\in E(G),h(e)>0\}. Let and be two sets of independent edges of with , and . If admits a fractional -factor such that for any and for any , then we say that has a fractional -factor with the property . In this paper, we present a neighborhood condition for the existence of a fractional -factor with the property in a graph. Furthermore, it is shown that the neighborhood condition is sharp
A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs
Let be a graph of order , and let and be two integers with . Let be a function. If holds for any , then we call a fractional -factor of with indicator function , where F_h = \{ e \in E(G) : h(e) > 0 \} . A graph is fractional independent-set-deletable -factor-critical (in short, fractional ID--factor-critical) if has a fractional -factor for every independent set of . In this paper, it is proved that if , and for any two nonadjacent vertices , then is fractional ID--factor-critical. Furthermore, it is shown that this result is best possible in some sense
- …